论文信息 - The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure

The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure

We show that the self-affine sets considered by McMullen in [ 11 ] and by Bedford in [ 1 ] have infinite Hausdorff measure in their dimension, except in the (rare) cases where the Hausdorff dimension coincides with the Minkowski (≡ box) dimension. More precisely, the Hausdorff measure of such a self-affine set K is infinite in the gauge (where γ is the Hausdorff dimension of K , and c > 0 is small). The Hausdorff measure of K becomes zero if 2 is replaced by any smaller number in the formula for the gauge o.

Yuval Peres | Y. Peres

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